Forecasting the copper price volatility is an important yet challenging task. Given the nonlinear and time-varying characteristics ofnumerous factors affecting the copper price, we propose a novel hybrid method to forecast copper price volatility. Two important techniques are synthesized in this method. One is the classic GARCH model which encodes useful statistical information about the time-varying copper price volatility in a compact form via the GARCH forecasts. The other is the powerful deep neural network which combines the GARCH forecasts with both domestic and international market factors to search for better nonlinear features; it also combines the long short-term memory (LSTM) network with traditionalartificial neural network (ANN)to generate better volatility forecasts. Our method synthesizes the merits ofthese two techniques and is especially suitable for the task of copper price volatility prediction. The empirical results show thatthe GARCH forecasts can serve as informative features to significantly increase the predictive power of the neural network model, and the integration of the LSTM and ANN networks is an effective approach to construct useful deep neural network structures to boost the prediction performance. Further, we conducted a series of sensitivity analyses of the neural network architecture to optimize the prediction results. The results suggest that the choice between LSTM and BLSTM networks for the hybrid model should consider the forecast horizon, while the ANN configurations should be fine-tuned depending on the choice of the measure of prediction errors.